An efficient parallel high-order compact scheme for the 3D incompressible Navier-Stokes equations

• Published in: International journal of computational fluid dynamics Vol. 31; no. 4-5; pp. 214 - 229
• Main Authors: Abide, S., Binous, M. S., Zeghmati, B.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 28.05.2017; Taylor & Francis Ltd
• Subjects: Accuracy; compact finite difference schemes; Computational fluid dynamics; Computer simulation; Computing time; Conservation; Cores; Decomposition; Derivatives; diagonalisation method; Error analysis; Finite difference method; Flow control; Fluid flow; high-performance computing; Incompressible flow; kinetic energy conservation; Mathematical models; Navier-Stokes equations; Numerical simulation of turbulent flows; Parallel processing; Physics; Stokes law (fluid mechanics); Turbulence
• ISSN: 1061-8562; 1029-0257
• DOI: 10.1080/10618562.2017.1326592

This article provides a strategy for solving incompressible turbulent flows, which combines compact finite difference schemes and parallel computing. The numerical features of this solver are the semi-implicit time advancement, the staggered arrangement of the variables and the fourth-order compact scheme discretisation. This is the usual way for solving accurately turbulent incompressible flows. We propose a new strategy for solving the Helmholtz/Poisson equations based on a parallel 2d-pencil decomposition of the diagonalisation method. The compact scheme derivatives are computed with the parallel diagonal dominant (PDD) algorithm, which achieves good parallel performances by introducing a bounded numerical error. We provide a new analysis of its effect on the numerical accuracy and conservation features. Several numerical experiments, including two simulations of turbulent flows, demonstrate that the PDD algorithm maintains the accuracy and conservation features, while conserving a good parallel performance, up to 4096 cores.